Monty Hall Problem (statistics/choice game)

[Defiant47]

8 random people walk up to Masquerouge:

2 of them have 2 sons, they both tell Masquerouge they have one son. masq guesses the other child is a daughter. He is wrong both times.

4 of them have both a son and a daughter, two tell Masq they have one son, two that they have one daughter, in all four instances Masq correctly guesses that the other child is the opposite sex.

2 of the mysterious strangers have two daughters and tell Masq they have one daughter. In both instances Masq wrongly guesses that the other child is a son.

50/50 win rate. Same as a random guess.

Excellent, now you capiche

To be fair, the problem is quite different to Monty Hall. In the Monty Hall problem, it doesn't matter if he deliberately picked the door with the goat, or if he picked it by random and it just so happened to be the goat -- you're still better off switching. That's what was confusing me...

Yes, it is entirely separate from Monty Hall. Sorry if that confused you

pquote]I accept now that how/why he picked his daughter makes a difference. If out of the 200 people, we asked, "do you have a daughter," then it'd be 2/3 for a son. If we just asked, "what is the gender of one of your children," then it'd be 1/2.

But if someone came up to me on the street and said, "I have two kids, one of them is a daughter, what's the other one?" I'd probably say daughter, cos I reckon he's trying to trick me.[/QUOTE]

If some stranger came in the street to tell me that, I would look at him, then depending on what he looks like, either run away real quick, or else tell them "go bother someone else, you freak,".

I mean, a stranger who tells me that is either a madman and possibly dangerous, or a trollish uber-geek. Either way, my geekiness has limits, and they're on the wrong side thereof.

Psh! Try going up to a stranger in the middle of the street and asking if they like to fly kites...

 

[brennan]

Excellent, now you capiche

Yeah, it's a subtle difference in the way the information is obtained that makes the difference. Clever.

 

[Masquerouge]

They sort of have a point - if you formulate the problem in such a way that anyone with at least one daughter, will tell you daughter, then the problem works. However, if you formulate it in such a way that people with one child of each gender get a choice of which gender's child they tell you about, then the problem introduces a whole host of new factors (cultural bias toward one gender or another, for a start).


(Note that meeting a girl in the street falls on the "choice" side - that is, they get to chose which child they go out with)

In the end, though, arguing over it is sort of futile. Posting this problem online, outside dedicated statistics forums, is a case of borderline trolling to begin with - you don't post it to get any serious discussion started, you post it (and Masque's various "will not argue" posts makes that fairly clear) to get an argument started (and mock people on the "non-statistician" side of the argument).

Which means they'll never back down - they'll just consider you a moron who won't listen to reason and keep arguing semantics rather than bowing before their Almighty Logic.

These forays into semantics and formulations are indeed what heats up the debate. What bugs me in the case of my wife is that we went through the exact same studies and thus have the exact same statistical background, and yet she persists in her errant ways.

 

[Defiant47]

These forays into semantics and formulations are indeed what heats up the debate. What bugs me in the case of my wife is that we went through the exact same studies and thus have the exact same statistical background, and yet she persists in her errant ways.

You have a statistical background?? How could you possibly decree that it's 2/3 then? Independence alone would be a sufficient claim to somebody with knowledge of statistics.

 

[Masquerouge]

You have a statistical background?? How could you possibly decree that it's 2/3 then? Independence alone would be a sufficient claim to somebody with knowledge of statistics.

nice!